How to resolve a vector into two directions not along the x or y axis?

I want to resolve a vector (I know its magnitude and angle referenced from the standard position) into two other vectors but not along the x- and y- axis. The two resolved vectors will still be perpendicular to each other though. Example:





I may want to resolve a vector of magnitude 10 in direction 40 degrees from standard position into two vectors – one at say 20 degrees and 110 degrees. Thanks.|||That's no problem.


One angle will be 20 deg. and other 70 deg. to this vector.


Resolving along these, vector parallel to 20 deg will be 10cos20 = 9.37


The vector in the direction parallel to 110 deg will be 10 sin 20=3.42.